Problem: Reduce to lowest terms: $- \dfrac{2}{7} \div - \dfrac{2}{5} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{2}{5}$ is $- \dfrac{5}{2}$ Therefore: $ - \dfrac{2}{7} \div - \dfrac{2}{5} = - \dfrac{2}{7} \times - \dfrac{5}{2} $ $ \phantom{- \dfrac{2}{7} \times - \dfrac{5}{2}} = \dfrac{-2 \times -5}{7 \times 2} $ $ \phantom{- \dfrac{2}{7} \times - \dfrac{5}{2}} = \dfrac{10}{14} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{10}{14} = \dfrac{10 \div 2}{14 \div 2} = \dfrac{5}{7} $